Over 47.5 points at +110 on one sportsbook, Under 47.5 at +100 on another. Put $97.56 on the Over and $102.44 on the Under, and either result returns $204.88 on $200.00 staked. That $4.88 is an arbitrage: a profit that does not depend on the score, as long as both bets stand.
The arbitrage betting calculator above finds the split. Enter the two prices and a total stake, and it shows whether the prices add up to less than 100%, how much to put on each side, the return either way and the profit as a percentage. It also says plainly when there is no arbitrage, which is almost always.
How to use the arbitrage betting calculator
Enter the best price available on each side of one market. Both prices have to describe exact opposites: Over and Under on the same total, the two moneylines in a sport with no draw, or the two sides of the same spread number. Then enter the total amount to stake across both bets.
The output shows the sum of the implied probabilities, the stake for each side, the payout that either result returns, the profit in dollars and the return on the total stake. If the sum is 100% or more, the result is shown as a loss, with the amount that covering both sides would cost.
The formula
Every number on the calculator comes from the implied probabilities of the two prices.
| Step | Calculation |
|---|---|
| Implied probability of each side | 1 ÷ decimal odds |
| Sum | side A + side B |
| Arbitrage exists when | sum < 100% |
| Stake on a side | total stake × that side’s implied probability ÷ sum |
| Payout either way | total stake ÷ sum |
| Return on stake | 1 ÷ sum − 1 |
The stakes are set so that each side’s stake times its decimal odds equals the same payout. Nothing about the formula requires two sportsbooks, but in practice a single book rarely if ever posts both sides of a market below 100%.
Worked example, then the usual case
The opening example in full: Over at +110 is 2.10 in decimal and implies 47.62%. Under at +100 is 2.00 and implies 50.00%. The sum is 97.62%.
| Side | Price | Implied | Stake from $200 | Return if it wins |
|---|---|---|---|---|
| Over 47.5 | +110 | 47.62% | $97.56 | $97.56 × 2.10 = $204.88 |
| Under 47.5 | +100 | 50.00% | $102.44 | $102.44 × 2.00 = $204.88 |
Payout is $200.00 ÷ 0.9762 = $204.88, a profit of $4.88, or 2.44% of the total stake.
Now the case the calculator sees far more often. A standard -110 / -110 line, even split across two books at the same price, sums to 104.76%. Staking $200.00 across it returns $190.91 whichever side wins, a certain loss of $9.09. That loss is the margin, and it is the reason true arbs are rare: every sportsbook builds its prices to sum above 100%, and a gap only opens when two books disagree by more than both of their margins combined.
Where arbs come from, and how long they last
A real arbitrage needs two sportsbooks to disagree, and to disagree enough to overcome the vig on both sides. That happens in a few situations. One book is slow to move after news, such as a lineup change. One book shades a line to attract action on one side. One book posts a price that is simply wrong.
All three close quickly. Sportsbooks watch each other and the wider market, and a price that is out of line with everyone else tends to move within minutes. The typical gap is small, a few percent of the stake or less, and anything much larger is more likely an error that will be voided than a gift.
Promotional price boosts are a fourth source. A boost lifts one side of a market above the normal line, and paired with the best regular price on the other side it can push the sum under 100%. Boosts usually come with a low maximum stake, so the profit in dollars stays small, and the boost terms decide how the bet settles.
Live markets add their own twist. After a big play, books reprice at different speeds, so for a few seconds one of them can show a price that the others have already moved past. That looks like an arbitrage on screen. In practice it is usually a stale line, and stale lines are exactly what bet delay and in-play acceptance checks exist to catch. The second bet in a live arb is the one most likely to be rejected or re-priced, and the bet delay guide explains how that window works.
The risks that the profit figure leaves out
The profit on the calculator assumes four things: both bets are accepted, at the prices entered, for the full stakes, and both settle by the same rules. Each assumption fails in practice often enough to matter.
Rejected or re-priced bets. If the second bet is rejected or offered at a worse price, the first bet is now an ordinary open position. Suppose the Under in the example moved from +100 to -110 before it was placed. With $97.56 already on the Over at 2.10, covering it at 1.9091 to match the $204.88 return takes $107.32, for a total stake of $204.88 and a profit of exactly $0.00. One price change turned a 2.44% arb into a break-even, and a second change would have turned it into a loss.
Palps and voids. Sportsbooks’ house rules generally let them void a bet placed at an obvious error in the price, usually called a palpable error or “palp”. Arbs built on a mispriced line are the most exposed to this. If the outlying side is voided, the other side stays live as a full-sized single bet, and the bettor is now carrying risk that was never part of the plan.
Different settlement rules. Two books can settle the same event differently. Tennis matches that end in a retirement, games that are suspended and finished later, and props on a player who leaves early are common examples. Read the rules for the market at both books before treating the position as closed.
Limits and account restrictions. Sportsbooks can cut the maximum stake on any account under their terms, and accounts that regularly take the outlying price on markets are frequent targets. A limit can arrive between the first and second bet, leaving the position half-built. Over time, limits make the strategy hard to repeat at all.
Money tied up at several books. An arb needs funded accounts at every sportsbook involved, because there is no time to deposit once the gap appears. That capital sits idle between opportunities, and the winning side’s payout lands at one book while the losing stake left another. Rebalancing means withdrawals and deposits, each with its own processing time. If you count the return on all the money parked across accounts, not only on the $200.00 in play, a 2.44% arb is a much smaller figure.
Put together, these risks mean the 2.44% on screen is a ceiling, not an expected return. One voided $100 leg erases the profit of dozens of successful small arbs.
Three-way markets and the side-track of the middle
Soccer match results, and any market with a draw, have three outcomes. The calculator takes two prices, but the method extends directly. Suppose the best prices across three books are home 2.60, draw 3.70 and away 3.10. The implied probabilities are 38.46%, 27.03% and 32.26%, a sum of 97.75%. A $300.00 total splits as $118.04, $82.95 and $99.01, and each outcome returns about $306.92, a profit near $6.92 or 2.31%. Rounding the stakes to cents moves each return by a cent or two.
A close cousin of the arb is worth knowing because it often shows up on the same screen. When two books post different numbers instead of different prices, for example Over 47.5 at one and Under 48.5 at the other, there is no locked-in profit. There is a middle: if the game lands exactly on 48 points, both bets win. Outside that number one wins and one loses, and the cost is roughly the margin. Middles are a bet on a specific result, and the calculator does not price them.
When the arbitrage betting calculator is still useful
Even for bettors who never try an arb, the tool has a practical job: it is the fastest way to see how much two sportsbooks’ prices disagree. A sum of 104.76% on a standard line is normal. A sum of 101% between two books means at least one is offering a price better than the usual margin, which is worth knowing before betting either side. A sum under 100% means someone is likely about to move. Usually quickly.
It also works as a check on a hedge placed at a second book. If you hold a pregame ticket and the live price elsewhere has moved enough, the two prices together may sum under 100%, and the hedge calculator and this tool will agree on a locked result. The arbitrage view simply starts from a total stake instead of from an existing ticket.
One number to keep in mind: at a 2.44% gap on $200.00, it takes almost two successful arbs to make back the $9.09 lost by splitting the same money across one standard -110 line.